As we move from numeracy into number sense, one of the most important things we need students to understand is our place value system.
Typically, we start off our year learning about place value, reviewing from last year and then building on that. This year might look different for you, especially if you are extending your review of last year’s standards that students may have missed during COVID.
Even if you find yourself reviewing, I think number sense is at the forefront of what students need to understand, and you can absolutely make a connection from numeracy going into place value. Yes, even in 5th grade!
Place Value Vocabulary
Let’s start at the very beginning – place value basics. This means the terminology we’ll use as we explain place value to our students. It is vitally important to have a universal language in your building as you approach this concept. There are three main terms, and our Place Value Basics video will help as we ensure that we’re naming things properly.
What is a “digit”? Many students will say it’s a number, but that’s not completely accurate because a number really goes to infinity. A digit represents the 10 numerals that we have in our number system: 0,1, 2, 3, 4, 5, 6, 7, 8, and 9. When discussing place value, we want to be careful to use either digit or numeral when we’re referring to the parts of a number. For example, if we had the number 542, you would not ask a student “What number is in the 10s place?” Instead, you would ask, “What digit or numeral is in the 10s place?” and in this case the answer would be 4.
What does place mean? The place is where a digit or numeral lives. Does it live in the 100s place? The 1000s place? The 1s place? When we’re talking about decimals, is it living in the 10ths place? The 100ths? Or the 1000ths place?
What does value mean? It means how much the digit is worth. To help students understand this concept, I thoroughly enjoy using the place value strips because the strips allow students to show or prove the value of their digit.
Let’s go back to 542. What is the value of the 4? Using place value strips, students could show that the 4 is actually worth 40.
The Right Tool for the Job
Think back for a second to the tools that you’ve used in your teaching career. I vividly remember teaching place value with a spiral-bound flipchart type thing that sat propped up in a triangle on the table. It was labelled at the top – 1,000,000s, 100,000s, 10,000s, 1000s, and so forth. I had all the digits in each place, and I could flip them around to build a number to show the students. if I wanted to say add 10 more, I would just flip a number in that place.
BUT…as I look at that chart now, can you see what may not be the most useful tool for helping kids understand the WHY before the HOW? The all-in-one place value flip chart certainly was a novel concept. And, yes, I can use it to point out the digit in a specific place, and even to help students see the different places, but when it comes to value, the old-school flip chart falls flat. If If I’m asking students to find the value of the 5 in the 100s place, they can’t separate that 5 to see the value is actually 500 like you can with place value strips.
That’s why I feel that student size place value strips are probably one of the most valuable tools that you can use during your place value unit. Giving students the ability to manipulate digits, build numbers, and apply vocabulary is vitally important. Talking about the digits and values helps students to be able to explain their thinking and start to conceptualize the idea of place value. Without this experience, place value it’s all very abstract.
Not sure where to start? This week’s collection of PowerPoints is going to show you a series of activities for second grade (whole numbers in the 10s and 100s), third grade (whole numbers up to 1000s), and then for fourth and fifth grade that will use whole numbers (up to 1000s in 5th grade) and decimals (10ths and 100ths). Both the PowerPoints and the video tutorials will walk you through the process of getting students to be able to build a number, and then to manipulate it. I love watching students problem-solve through building a number and asking questions about the number and their process – it truly shows their depth of understanding!
Using Place Value Strips in the Classroom
When using place value strips in your classroom, we like to have students work in pairs. Designate one student to be the clip captain. This student will be in charge of manipulating the mini binder clips that serve as a stand for the place value strips once the number is built. This same student will also be in charge of the 1s and the 10s. The other student will be in charge of the 100s and 1000s. As you call out numbers to build, they will work together to create it using their places.
If your students are virtual, students can do this on their own and show you their place value strips on their screen. Many of our schools have created mini math toolkits that students can take home, and one of the things the kits always include are the place value strips!
Many of the activities we talked about in our blog last week can get things rolling and create that bridge from numeracy to place value. You might show your number on an abacus, or two abaci to show numbers into the hundreds, and have students build with the place value strips.
Once the number is built, you can ask students questions such as “What place is the 3 in?” Then, using the strips, students can show that digit and talk about the place. You could ask, “What is the value of the 4 in your number?” and students can prove the value by pulling apart their place value strips to show you what it looks like.
Place value discs, the whole numbers and the decimal tiles, would also work well to get kids to see the quantity of how to build numbers.
Place Value and Expanded Form
I find that showing expanded form is one of the most fun parts about using the place value strips. If you ask students to read a number that we’re talking about and then show the expanded form, many times they have trouble visualizing that. But, if you are able to pull the number completely apart and see that it is really 4000 + 500 + 30 + 2, which equals 4532, the lightbulbs usually go off! The video explains the whole process of how we can help students understand that correspondence.
Our tutorial videos – featured on our M3 Membership site or available as a bundle in our store – will walk you through the entire process for each grade level, but you can do any of the activities with any of the place values! The goal is for students to be able to build their number and articulate their reasoning as they manipulate it.
Getting kids comfortable with playing with place value will help as we start looking at the idea of “more or less” – taking a number and building it a certain amount more or less. It will even be useful when we get to that really tricky topic of rounding a few weeks down the road! Join us next week to see what we have in store for you as you continue your place value instruction!